MOORE, Okla.—Violent tornadoes swept through towns just south of Oklahoma City Monday afternoon, killing at least 51 people, including at least 20 children, and laying waste to numerous buildings, including more than one elementary school.

One tornado leveled Plaza Towers Elementary, a school in Moore, a city of 55,000 people about 15 miles south of Oklahoma City, the state capital. Jerry Lojka, an official with the Oklahoma Department of Emergency Management, said Monday evening that rescue workers were "trying to turn...